Andrew Russell Forsyth by Leonard Roth

An extract from the paper : L Roth, Amer. Math. Monthly (1971)

This extraordinary man, whom I had the privilege to know in his capacity of Professor Emeritus at the Imperial College of Science, died in extreme old in 1942; but his fame lives on. Everybody knows him as the author of the age in most successful book on differential equations that has ever appeared in any language; although it was first published as long ago as 1885, it is still being reprinted. I would venture the opinion that this work has done more than anything else to retard the true development of the subject; for over two generations it has continued to put wrong ideas into people's heads concerning the nature and scope of the theory and, thanks to the author's forceful and authoritative style, in this it has been overwhelmingly successful.

The truth is that Forsyth had the misfortune to be born a hundred years too late; in his mathematical outlook and technique, he was a man of the eighteenth century. His major work on the theory of differential equations, a colossal achievement in six volumes, is still today the only treatise in its class which in by a single hand; but a mere glance at the list of contents suffices to reveal that, on the whole, Forsyth looks backward to Lagrange rather than forward to Cauchy. However, some knowledge of the rudiments of analysis was essential to an understanding of the work; and as the Cambridge men of his generation had none, the author, who had now succeeded to Cayley's chair, set himself the task of educating them. ...

In 1893 there appeared the first edition of Forsyth's Theory of Functions of a Complex Variable: another production which cannot be described as anything less than colossal - even a German professor might have quailed before such a project. The book includes fairly complete accounts of the relevant work of Cauchy, Abel, Riemann, Weierstrass, Appell, and carries on the survey right up to the then contemporary researches of Klein and Poincaré. The style of the book is magisterial, Johnsonian; the author's powers of assimilation are well-nigh incredible and yet, strange to say despite his intentions and his absorption of the material, he never comes within reach of comprehending what modern analysis is really about: indeed whole tracts of the book read as though they had been written by Euler.

Nevertheless, for all its shortcomings, this was the work which brought modern pure mathematics into Cambridge. The young men at once began to imbibe it; and not the young men alone. My own copy of the book once belonged to R R Webb, the coach whom I have mentioned above and from his pencilled notes in the margins it seems pretty clear that he was learning his function theory the hard way, much as any beginner would. The very fact that the book was written in the wrong spirit probably contributed to its great initial success. As Littlewood once put it, "Forsyth was not very good at delta and epsilon"; but neither was the public for whom he wrote: so author and readers met on common ground. In any case, it served as a stepping-stone to the real thing, which at that date was to be found only in French or German. Hardy has recorded that he himself first saw the light when he read the volumes of Jordan's Cours d'Analyse; and many other young men of his generation must have done likewise.

Within the space of ten years, Forsyth's treatise had achieved its aim. But it also accomplished something which its author had certainly never intended. For Cambridge now found itself equipped with a corps of modern pure mathematicians whose nominal leader was a living fossil firmly fixed in the Sadlerian chair. This grotesque situation seemed to all intents and purposes a permanent one: Forsyth's international reputation was enormous and in any case there was no possibility of removing him; it appeared as though he were there for life. But now fate took a hand in the game. In the year 1909 Forsyth in the company of other scientists and their families, was travelling to a meeting of the British Association to be held in Canada. Among the party were the eminent physicist C V Boys and his wife Marion. Forsyth was then an apparently confirmed bachelor of 51; but he and Marion Boys fell in love with one another. The end of it was that she decided to leave her husband; and this meant that Forsyth was compelled to resign his professorship, for in the Cambridge of those days there was no place for even the suggestion of divorce. It is pleasant to add that everyone concerned in this affair lived happily ever after; for it was generally conceded by all his acquaintances that the bereaved husband bore his loss with remarkable fortitude. (The former Mrs Boys was a powerful personality.)

Forsyth survived his wife by many years; in fact he contrived to outlive everything-that was his tragedy. He had to retire from his chair at the Imperial College because he had reached the extreme age limit, although he commanded enough energy to have carried on for at least another five years. He set himself to learn Arabic and Persian; he wrote several enormous volumes on what were ostensibly branches of modern mathematics all treated from the eighteenth century point of view; the Cambridge University Press, which made a fortune out of his earlier publications must have lost a good deal of it on these. And all the time he was filling reams of paper with formulae and calculations; I happen to possess some manuscripts of his Cambridge lectures and also of sonic work on which he was engaged a year or two before his death. The differences between them, from the standpoint of calligraphy, are almost negligible.

I am pleased to relate that I have been able to pay one small tribute to this remarkable son of Cambridge. Some years ago, when I was asked to rewrite the article on Cayley for the Encyclopaedia Britannica, I took the opportunity to slip him in; and there, for some time to come, I hope he will stay.

... Although it almost goes without saying that Forsyth had himself been a Senior Wrangler (he had studied with Routh and Webb) and, moreover, was temperamentally inclined towards the Tripos kind of mathematics, yet he was one of the chief promoters of Tripos reform.

JOC/EFR October 2003

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